Perspective machine



July 25, 1967 5, gnu

PERSPECTIVE MACHINE 5 Sheets-Sheet l Filed April so, 1965 I TI 5 l R M m SIDNEY BY July 25; 1967 RU 3,332,152

PERSPECTIVE MACHINE Filed April :50. 1965 5 Sheets-Sheet 2 I? 2 w "n v k x 3 V \1 N u,

INVENTOR. SIDNEY DPU BY w km ATTORNEYS United States Patent 3,332,152 PERSPECTIVE MACHINE Sidney Dru, Brooklyn, N.Y., assignor to Dru Enterprises Inc., Seaford, N.Y., a corporation of New York Filed Apr. 30, 1965, Ser. No. 452,154 16 Claims. (Cl. 33-77) My invention relates to drafting engines and more particularly to perspective machines.

One perspective machine of the prior art employs a quadrilateral linkage having two long opposite sides of equal length and two short sides. One of the short sides is adjustable. The vanishing point is disposed orthogonally to one of the short sides. The machine is of simple construction but has the inherent defect that the linkage geometry does not produce true perspective, for that movement of the linkage causes a shift in the vanishing point which becomes more and more serious with displacement from a trapezoidal disposition.

Another perspective machine of the prior art overcomes this defect by providing a quadrilateral linkage having two long opposite sides of equal length, one fixed side, and a side of variable length together with a synchronizing mechanism for insuring that the angular increments of motion of the two long sides are equal. Again the vanishing point is disposed orthogonally to one of the short sides. Such machine is capable of producing true perspective; however, the synchronizing mechanism introduces additional expense.

A further perspective machine of the prior art employs a trapezoidal linkage in which two opposing sides are maintained parallel. Such machine is inexpensive and produces true perspective. However, the machine must be positioned on the drawing board where it obscures the working surface and it can produce only those portions of the perspective view which are, for example, above the horizon. In order to produce those portions of the perspective view below thehorizon it is necessary either to reposition the machine or to employ another trapezoidal linkage.

One object of my invention is to provide a trapezoidal perspective machine which is mounted oif the drawing board and does not obscure the working surface.

Another object of my invention is to provide a trapezoidal perspective machine which can produce portions of a perspective view both above and below the horizon.

A further object of my invention is to provide a trapezoidal perspective machine which may be readily and.

accurately adjusted to provide and hold any desired vanishing point.

Other and further objects of my invention will appear from the following description: 1

In general my invention contemplates the provision of a parallel motion linkage having two oppositely disposed long arms of equal length and two oppositely disposed short arms of equal length. One of the short arms is disposed coincident with the locus of vanishing points and is positioned off the drawing board at a fixed location. A rule is pivotally mounted at the junction of one of the long arms and the movable short arm. The rule is provided with a slide which coacts with a pivot mounted on a cursor carried by the other long arm. From the construction thus far described it will be appreciated that when the rule is coincident with the horizon comprising the locus of vanishing points, then all portions of the parallelogram are oolinear; and, from the linkage geometry, there exists the possibility of an ambiguity. With motion of the rule from above to below the horizon, for example, the movable short arm may on one hand retain the desired parallel relation with the fixed short arm so that the long arms remain parallel or, on the other hand, the movable short arm may rotate relative to the fixed short arm so that the two long arms cross. In order to obviate the latter alternative and eliminate ambiguity in the linkage geometry I provide a third long arm of equal length to the other two. This third arm is pivoted adjacent the fixed short arm either above or below the horizon, the two ends of the fixed short arm and the pivot of the third long arm thereby defining a first triangle. The third arm is also pivoted adjacent the movable short arm at a point such that the two ends of the movable short arm and the other pivot of the third arm define a second triangle congruent to the first. Thus I provide a three link parallel motion assembly. The third arm introduces a redundancy which eliminates ambiguities in the linkage geometry when the rule is moved through the horizon.

In the accompanying drawings which form part of the instant specification and which are to be read in conjunc-,

tion therewith and in which like reference numerals are used to indicate like parts in the various views:

FIGURE 1 is a plan view of a first embodiment of my invention.

FIGURE 2 is a diagrammatic view showing the geometrical relationships which are observed in holding a fixed vanishing point.

FIGURE 3 is a diagrammatic view showing the production of a perspective view having portions both above and below the horizon and having vanishing points both to the left and to the right of the drawing board.

FIGURE 4 is a plan view of a second embodiment of my invention.

FIGURE 5 is a sectional elevation taken along the line 5-5 of FIGURE 4.

FIGURE 6 is a fragmentary plan view showing one a pair of feet 13 and 14 to which is attached an exten sion member 12 mounting a fixed support 15 having triangularly disposed pivots D, E, and 18. The spacing between pivot E and the left-hand edge of the drawing board may be twelve inches. Pivots D and E are coincident with the horizon H which comprises the locus of vanishing points and may be spaced apart four inches. A movable triangular support 20 is provided with pivots A, C, and 19. Arms 17 and 16 are mounted above extension member 12 and beneath supports 15 and 20. Arm 17 is journalled in pivots A and E; and arm 16, in pivots 19 .and 18. The length of each of arms 16 and 17 may be 21 which is positioned above supports 15 and 20. Arm' 21 may have a total length of sixteen inches of which eleven inches are included between pivots C and D. Arm 21 extends two inches beyond pivot C and extends three inches beyond pivot D. Pivots A, C, and 19 form a triangle which is congruent to the triangle formed by pivots E, D, and 18. Pivot 18 is disposed four inches above the horizon H and one-half inch to the left of pivot E. Arms 16 and 17 each have a width of one-half inch and operate in the same plane. In the position shown, arms 16, 17, and 21 are all disposed orthogonally to the horizon. Further counterclockwise movement of the movable support 20 is prevented because of the engagement of arms 16 and 17. A transparent rule 33 is connected by a mem- ;23. Arm 27 is provided with an elongated slot or slide 28. The width of slot 28 is substantially equal to the diameter of pivot B to provide a close sliding fit. Rule 33 is so mounted relative to arm 27 that an extension of its upper edge 33a passes through the centers of pivots A and B. Triangular support 20 is provided with a uniformly-graduated angular scale which is circularly disposed about pivot point A and has an index mark 31. Upon a lateral extension 29 of arm 27 is mounted a uniformlygraduated angular vernier scale which is provided with an index mark 30. The angular scale associated with index 31 may be graduated in 1 increments. The vernier scale associated with index 30, as will be appreciated by those ordinarily skilled in the art, is used for interpolating to any desired fraction of a degree, such as 0.1". Accordingly, the vernier scale is provided with ten equally spaced marks which subtend only 9. Member 21 is provided with a uniformly-graduated rectilinear scale having an index 22. Upon an extension 25 of cursor 23 is mounted a uniformly-graduated rectilinear vernier scale which is provided with an index 26. The scale associated with index 22 may have ten divisions per inch. In order to divide each tenth of an inch into ten equal parts, the vernier scale mounted upon extension 25 should have ten equally spaced marks which extend through only nine-tenths of an inch.

The vanishing point may be set either by the rectilinear scale of arm 21 or the angular scale of support 20. The rectilinear scale of arm 21 may be used to set the vanishing point in any position of the movable support 20. However, the vanishing point can be set by the angular scale of support 20 only with support 20 in the extreme counterclockwise position shown where arms 16, 17, and 21 are disposed orthogonally to the horizon H. With cursor 23 in the position shown, the vanishing point P is eleven inches to the left of pivot E and hence twentythree inches to the left of the left-hand edge of the drawing board 10. If cursor 23 is moved upwardly so that the indices 22 and 26 coincide, then the indices 31 and 30 will also coincide; and pivot point B will be superposed upon pivot point C. With such an adjustment, the vanishing point is at infinity; and my perspective machine reduces to a simple parallel rule. When, as in the position shown, pivot B is below pivot C, then index 30 will be positioned counterclockwise of index 31; and the vanishing point is to the left of pivot E. If pivot B is moved above pivot C, then index 30 will be positioned clockwise of index 31; and the vanishing point will lie to the right of pivot E. Pivot B can be moved one inch above pivot C, as indicated by line M; and with such disposition, the position of the vanishing point may be determined by extending line m through point A where it intersects the horizon H forty-four inches to the right of pivot E. To accommodate this disposition of pivot B when drawing lines adjacent to or coincident with the horizon, slot 28 should extend within three inches of pivot A. I have shown slot 28 to extend within one and one-half inches of pivot A in order to provide an appreciable tolerance. When cursor 23 is moved downwardly so that pivot B is superposed upon pivot D, then the vanishing point is coincident with pivot D which lies four inches to the left of pivot E and hence sixteen inches to the left of the lefthand edge of the drawing board. The cursor can be moved further until pivot B is one inch below pivot D corresponding to line N. With such disposition, the vanishing point is positioned one-third inch to the right of pivot D as determined by the intersection with the horizon H of an extension of line n through pivot A. In order to accommodate this disposition of pivot B when drawing a line adjacent to or coincident with the horizon, slot 28 should extend at least sixteen inches from pivot A. I have shown slot 28 to extend sixteen and one-half inches from pivot A in order to provide an appreciable tolerance.

The rectilinear and the angular scales must have uniformly spaced marks in order to obtain vernier interpolations. However, the relationships between these linear functions and the corresponding position of the vanishing point is nonlinear. It will be appreciated that either one of the rectilinear and angular scales is suflicient to set the vanishing point. It will be further appreciated by those having ordinary skill in the art that where only the rectilinear scale is employed then the position of pivots 18 and 19 in conjunction with the widths of arms 16 and 17 need not be such that the limit of counterclockwise rotation of support 20 occurs with arms 16, 17, and 21 disposed at right angles to the horizon.

Referring now to FIGURE 2, I have shown a schematic view with arm 16 omitted to illustrate the essential geometrical relationships. Arms 17 and 21 are always maintained parallel. Accordingly the angle P] 3 B is equal to PEA. Also the angle PBD is equal to the angle PAE. The angle EBA is common to triangles PBD and PAE. Since the angles of triangle PBD are equal to the angles of triangle PAE, the two triangles are similar. For these similar triangles the following proportionality applies:

any All PE The following equation is true since both sides are equal to unity (2) EL E AE PE Subtracting Equation 1 from Equation 2 and combining terms, we obtain AE PE In FIGURE 1, AE=11 inches and the quantity PEPD=4 inches. Substituting these values in Equation 3 and simplifying, we obtain U 11 BD It will be noted that pivot B may extend one inch below pivot D. In order to avoid negative numbers, let the scale setting S in inches be defined as follows:

(5) S 1+BD Substituting Equation 5 in Equation 4 we find tan 0 tan PAE= Since AE=11 inches, Equation 7 reduces to PE=11 tan 0 Referring now to FIGURE 3, there is illustrated the drafting of a perspective view upon a paper 11 which is mounted on the surface of the drawing board 10. The lines R1 through R5 have a vanishing point which is to the right of the right-hand edge of the drawing board and are obtained by setting the cursor so that pivot B is disposed on that side of pivot C which is remote pivot D. The lines L1 through L5 have a vanishing point which lies to the left of pivot E and are obtained by setting the cursor so that pivot B is disposed on that side of pivot C which is adjacent pivot D. In FIGURES 2 and 3 it will be noted that the third arm 16, which eliminates ambiguity in the linkage of FIGURE 1 as member 20 moves through the horizon H, has not been shown to simplify the description.

Upon extension member 12 is placed one of a pair of tables 12a and 12b which relate the setting of one of 11: 9s 2, 200 12198 44: 90 11. 9s 4, 400 12.99 44. 45 12. 00 m 13. 00 44. 00

If the angular scale is employed, then the rectilinear scale need not be provided. Assuming that in the position shown the angular setting 0 is 45.0 and that with indices 30 and 31 coincident the angular setting 0 is 900, then employing Equation 8, table 1211 will appear as follows s9. 8 3, i51 10's. 9 44: 45 39. 9 6, 302 104. 0 44. 12 90. 0 m 104. 1 43. 79

It will be noted that the scales associated with indices 22 and 31 may have non-linear graduations. In such event no vernier scales need be provided for indices 26 and 30; and conversion tables 12a and 12b may be eliminated. The provision of such non-linear gr-aduations permits of the direct reading of the position of the vanishing point, but with a correspondingly reduced accuracy.

Referring now to FIGURES 4 and 5, there is shown an alternative embodiment of the invention which, however, is not suitable for the angular scale associated with indices 30 and 31. The pivots of supports 15a and a form triangles which are symmetrically disposed about the horizon H. Pivot E of support 15 is replaced by a pivot 38a in support 15a. Arm 17a connects pivot 38a with a corresponding pivot 39a in support 20a. Pivots 18a and 38a are aligned along a common normal to the horizon, as are pivots 19a and 39a. With the construction shown in FIGURE 4, arm 17a never coincides with the horizon as does arm 17 in FIGURE 1. In FIGURE 4 arm 27 is journalled at pivot A in support 20a. If arm 1711 were omitted, then the linkage of FIGURE 4 would exhibit ambiguity when rotated 30 counterclockwise from the position shown. If arm 16a were omitted, then the linkage would exhibit ambiguity when rotated 30 clockwise from the position shown. The provision of the three parallel arms 21, 16a, and 17a removes both these linkage ambiguities. Because of the parallel motion provided by the three arms there arises on support 15a a virtual pivot e equivalent to pivot E of FIGURE 1, since the distance from pivot A to virtual pivot 2 remains constant at eleven inches irrespective of movement of support 20a.

Referring now to FIGURE 5, my perspective machine is secured to the drawing board 10 by a thumbscrew 42 which causes a foot 43 to engage the undersurface thereof. Thumbscrew 42 and foot 43 are disposed underneath foot 13. A similar thumbscrew and foot are disposed under foot 14. Shaft A is extended above the plane of arm 27 to receive a cam 50 which coacts with a corresponding vertical extension of pivot B. In order to employ cam 50 for setting the vanishing point, the machine is placed in the position shown in FIGURE 4 where the edge 33a of rule 33 is coincident with the horizon. This will occur when arms 16a and 17a lie parallel to extension member 12. This parallel relationship is readily established visually to within a fraction of a degree. It will be appreciated that while a detenting mechanism may be used to establish this parallel relationship, a misalignment from parallelism of as much as one degree will produce an error in the position of the vanishing point of less than two parts in ten thousand.

Cam 50 may comprise a linear spiral as shown in FIGURE 6 which is adapted to be rotated through 180. At the point on the cam, Where the radius is nominally four inches, there is provided an index 51. At the 0 point of cam 50 the nominal radius is three inches; and at the point, where pivot B is shown engaging the cam, the radius is nominally five inches. As indicated in FIGURES 4 and 6, pivot B is provided with a scribe mark which is brought into registration with a desired one of the indicia provided on the circumference of cam 50. The cursor is moved until pivot B engages the periphery of the cam and then thumbscrew 24 is tightened. In the positions shown in FIGURES 5 and 6, pivot B is posi tioned five inches from pivot A. Since the distance between pivots A and C is four inches, this corresponds to a setting of pivot B which is one inch from pivot C on that side of the pivot adjacent pivot D. In FIGURE 1 this would correspond to a scale reading S of eleven inches which in turn corresponds to a vanishing point 44.00 inches to the left of either pivot E in FIGURE 1 or virtual pivot e in FIGURES 4 and 5. It will be appreciated that the actual radii of cam 50 corresponding to the angular positions indicated must be reduced by one-half the diameter of pivot B in order that the distances between the centers of pivots A and B be correct. Because of the large expansion of scale afforded by cam 50 the vanishing point distances from pivots E or e may be read directly with high accuracy. No vernier need be employed; and the scale need not be linear.

Referring now to FIGURE 7, there is shown an alternate cam 50a which is adapted to rotate through more than 360. Cam 50a provides an even larger expansion of scalethan ,does cam 50. At the 0 point of cam 50a, Where the radius is four inches minus the radius of pivot B, there is provided an index 51a. At the -90 point of cam 50a the radius is nominally three and one-half inches. At the --'1-80 point of cam 50a the radius is nominally three inches. At the +90 point the radius is nominally four and one-half inches; and at the +180 point, where pivot B is shown engaging the cam, the radius is normally five inches. Any number of cams may be employed to provide any desired degree of expansion of scale.

In FIGURE 4 I have shown normal projections of pivots 18a and 38a upon the horizon to be displaced onehalf inch to the left of virtual pivot e. Correspondingly, pivots 19a and 39a are similarly displaced to the left of pivot A. The purpose of this displacement is merely to clarify FIGURE 5. It is desirable, in order to achieve high accuracy, that the triangles defined by the three pivots on both the fixed and movable supports include the largest possible area. Accordingly pivots 18a and 38a and also 19a and 39a are preferably positioned in FIGURES 4 and 5 such that normal projections thereof upon the locus of vanishing points H are respectively coincident with virtual pivot e and with pivot A.

In FIGURE 5 there has been shown the angular vernier 29, although as previously indicated the arrangement of pivots 18a, 19a, 38a, and 39a does not afford sufficient movement of support 20a to position arms 16a and 17a orthogonally to the horizon. As may be seen by reference to FIGURE 5 the bottom surface of the cursor 23 should be elevated sufficiently above the plane of the supports to permit a working space for movement of vernier 29 where, as in FIGURE 1, it may be employed. In FIG- URE 5 the rectilinear vernier 25 has been shown, since it may be used in all embodiments of the invention as either a supplement to or alternative for the use of the cams. The rectilinear scale may be used to set the vanishing point in any position of support 20 or 20a.

It will be seen that I have accomplished the object of my invention. My perspective machine is mounted off the drawing board and does not obscure the working surface. My machine employs a trapezoidal linkage which precisely holds a predetermined vanishing point. My machine is provided with a redundant arm which eliminates the occurrence of linkage ambiguities and permits the production of perspective views having portions both above and below the horizon. My perspective machine may readily establish vanishing points either to the left or to the right of the drawing board without requiring that the mounting position of the machine be changed. The vanishing point is readily set in any position of the machine by employing a rectilinear scale with or without a vernier. By setting the machine to a 90 position the vanishing point is readily set by employing an angular scale either with or without a vernier. By setting the machine to a position the vanishing point is readily set by employing one or more cams providing any desired degree of expansion of scale.

It will be understood that certain features and subcombinations are of utility and may be employed without reference to other features and subcombinations. This is contemplated by and is within the scope of my claims. It is further obvious that various changes may be made in details within the scope of my claims without departing from the spirit of my invention. It is, therefore, to be understood that my invention is not to be limited to the specific details shown and described.

Having thus described my invention, what I claim is:

1. In a perspective drafting machine having a ruling arm which coacts with an adjustable pivot, a fixed support having three pivots defining a first triangle, a movable support having three pivots defining a second triangle congruent to the first, three arms of equal length connecting corresponding pivots of the first and second triangles, and means for positioning said adjustable pivot at any point along a first of the three arms.

2. In a perspective drafting machine as in claim 1 wherein the first arm is provided with an appreciable extension beyond One of its pivots.

3. A perspective drafting machine including in combination a fixed support having three pivots defining a first triangle, a movable support having three pivots defining a second triangle congruent to the first, three arms of equal length connecting corresponding pivots of the first and second triangles, means for positioning an adjustable pivot at a certain point along a first of the three arms, a ruling arm provided with a slide engaging the adjustable pivot, and means journalling the ruling arm on the movable support.

4. A perspective drafting machine as in claim 3 in which the first arm is provided with a rectilinear scale and the positioning means is provided with a coacting index.

5. A perspective drafting machine as in claim 3 in which the first arm is provided with a rectilinear scale having uniformly-spaced graduations and the positioning means is provided with a coacting vernier scale.

6. A perspective drafting machine as in claim 3 in which the first arm is provided with an appreciable extension beyond one of its pivots.

7. A perspective drafting machine as in claim 3 in which the movable support is provided with an angular scale and the ruling arm is provided with a coacting index.

8. A perspective drafting machine as in claim 3 in which the movable support is provided with an angular scale having uniformly-spaced graduations and the ruling arm is provided with a coacting vernier scale.

9. A perspective drafting machine as in claim 3 which further includes a cam journalled at a point along the 0 ruling arm and coacting with the adjustable pivot to control the positioning thereof.

10. A perspective drafting machine as in claim 3 which further includes a cam journalled at a point along the ruling arm and coacting with the adjustable pivot to control the positioning thereof, the cam being provided with a scale along its periphery and the adjustable pivot being provided with a coacting index.

11. In a perspective drafting machine having a ruling arm which coacts with an adjustable pivot, a fixed support having three pivots defining a first triangle, a movable support having three pivots defining a second triangle congruent to the first, three arms of equal length connecting corresponding pivots of the first and second triangles, the length of the arms appreciably exceeding the distance between any two fixed support pivots, the supports being disposed in a first common plane, a first and a second of the arms being disposed for movement in a second common plane, the third arm being disposed for movement in a third plane, the three planes being parallel and the first plane being disposed intermediate the second and third planes.

12. In a perspective drafting machine as in claim 11 wherein the third arm is provided with an appreciable extension beyond one of its pivots.

13-. In a perspective drafting machine as in claim 11, means for positioning said adjustable pivot at a certain point along the third arm, said ruling arm being provided with a slide engaging the adjustable pivot, means journalling the ruling arm on the movable support, the ruling arm being disposed for movement in a fourth parallel plane, and the third plane being disposed intermediate the first and fourth planes.

14. In a perspective drafting machine as in claim 11, means for positioning said adjustable pivot at a certain point along the third arm, said ruling arm being provided with a slide engaging the adjustable pivot, means journalling the ruling arm on the movable support, a cam journalled at a point along the ruling arm and coacting with the adjustable pivot to control the positioning thereof, the ruling arm being disposed for movement in a fourth parallel plane, the cam being disposed for movement in a fifth parallel plane, the third plane being disposed intermediate the first and fourth planes, and the fourth plane being disposed intermediate the third and fifth planes.

15. In a perspective drafting machine having a ruling arm which coacts with an adjustable pivot, a fixed support having three pivots defining a first triangle, a movable support having three pivots defining a second triangle congruent to the first, three arms of equal lengths connecting corresponding pivots of the first and second triangles, a line defining the locus of vanishing points passing through a first of the fixed support pivots associated with a first of the arms, normal projections of the second and third fixed support pivots upon the locus intersecting the locus at points separated a predetermined distance, the second and third arms being disposed for movement in a common plane and having such widths that one-half the sum thereof is equal to said predetermined distance.

16. In a perspective drafting machine as in claim 15 wherein the first arm is provided with an appreciable extension beyond one of its pivots.

References Cited UNITED STATES PATENTS 2,854,750 10/1958 Pirogow 3377 FOREIGN PATENTS 2/1945 Italy. 1/ 1947 Italy. 

1. IN A PERSPECTIVE DRAFTING MACHINE HAVING A RULING ARM WHICH COACTS WITH AN ADJUSTABLE PIVOT, A FIXED SUPPORT HAVING THREE PIVOTS DEFINING A FIRST TRIANGLE, A MOVABLE SUPPORT HAVING THREE PIVOTS DEFINING A SECOND TRIANGLE CONGRUENT TO THE FIRST, THREE ARMS OF EQUAL LENGTH CONNECTING CORRESPONDING PIVOTS OF THE FIRST AND SECOND TRIANGLES, AND MEANS FOR POSITIONING SAID ADJUSTABLE PIVOT AT ANY POINT ALONG A FIRST OF THE THREE ARMS. 